Linear-Time Sum-Check

Definition ∞ A linear-time sum-check protocol is a cryptographic primitive used in zero-knowledge proofs. It enables a prover to convince a verifier that a polynomial evaluated over a hypercube sums to a specific value, with verification time linear in the number of variables. This protocol is foundational for constructing efficient interactive oracle proofs and polynomial commitment schemes. It significantly reduces the computational burden on the verifier, making verifiable computation more practical. This efficiency is critical for scalable blockchain solutions.
Context ∞ In zero-knowledge proof research and development, linear-time sum-check protocols are frequently discussed as a core component for improving the efficiency and scalability of zk-SNARKs and other verifiable computation systems. News in this domain often highlights new constructions or optimizations of sum-check protocols that yield faster proof generation or smaller proof sizes. These advancements are crucial for the widespread adoption of privacy-preserving and scalable blockchain applications.